Dynamical properties of a gene-protein model

A major limitation of the classical random Boolean network model of gene regulatory networks is its synchronous updating, which implies that all the proteins decay at the same rate. Here a model is discussed, where the network is composed of two different sets of nodes, labelled G and P with reference to “genes” and “proteins”. Each gene corresponds to a protein (the one it codes for), while several proteins can simultaneously affect the expression of a gene. Both kinds of nodes take Boolean values. If we look at the genes only, it is like adding some memory terms, so the new state of the gene subnetwork network does no longer depend upon its previous state only. In general, these terms tend to make the dynamics of the network more ordered than that of the corresponding memoryless network. The analysis is focused here mostly on dynamical critical states. It has been shown elsewhere that the usual way of computing the Derrida parameter, starting from purely random initial conditions, can be misleading in strongly non-ergodic systems. So here the effects of perturbations on both genes’ and proteins’ levels is analysed, using both the canonical Derrida procedure and an “extended” one. The results are discussed. Moreover, the stability of attractors is also analysed, measured by counting the fraction of perturbations where the system eventually falls back onto the initial attractor

A stochastic model of the emergence of autocatalytic cycles

Autocatalytic cycles are rather common in biological systems and they might have played a major role in the transition from non-living to living systems. Several theoretical models have been proposed to address the experimentalists during the investigation of this issue and most of them describe a phase transition depending upon the level of heterogeneity of the chemical soup. Nevertheless, it is well known that reproducing the emergence of autocatalytic sets in wet laboratories is a hard task. Understanding the rationale at the basis of such a mismatch between theoretical predictions and experimental observations is therefore of fundamental importance. We here introduce a novel stochastic model of catalytic reaction networks, in order to investigate the emergence of autocatalytic cycles, sensibly considering the importance of noise, of small-number effects and the possible growth of the number of different elements in the system. Furthermore, the introduction of a temporal threshold that defines how long a specific reaction is kept in the reaction graph allows to univocally define cycles also within an asynchronous framework. The foremost analyses have been focused on the study of the variation of the composition of the incoming flux. It was possible to show that the activity of the system is enhanced, with particular regard to the emergence of autocatalytic sets, if a larger number of different elements is present in the incoming flux, while the specific length of the species seems to entail minor effects on the overall dynamics

A stochastic model of the emergence of autocatalytic cycles

Autocatalytic cycles are rather common in biological systems and they might have played a major role in the transition from non-living to living systems. Several theoretical models have been proposed to address the experimentalists during the investigation of this issue and most of them describe a phase transition depending upon the level of heterogeneity of the chemical soup. Nevertheless, it is well known that reproducing the emergence of autocatalytic sets in wet laboratories is a hard task. Understanding the rationale at the basis of such a mismatch between theoretical predictions and experimental observations is therefore of fundamental importance. We here introduce a novel stochastic model of catalytic reaction networks, in order to investigate the emergence of autocatalytic cycles, sensibly considering the importance of noise, of small-number effects and the possible growth of the number of different elements in the system. Furthermore, the introduction of a temporal threshold that defines how long a specific reaction is kept in the reaction graph allows to univocally define cycles also within an asynchronous framework. The foremost analyses have been focused on the study of the variation of the composition of the incoming flux. It was possible to show that the activity of the system is enhanced, with particular regard to the emergence of autocatalytic sets, if a larger number of different elements is present in the incoming flux, while the specific length of the species seems to entail minor effects on the overall dynamics

Mathematical model of a telomerase transcriptional regulatory network developed by cell-based screening: analysis of inhibitor effects and telomerase expression mechanisms

Cancer cells depend on transcription of telomerase reverse transcriptase (TERT). Many transcription factors affect TERT, though regulation occurs in context of a broader network. Network effects on telomerase regulation have not been investigated, though deeper understanding of TERT transcription requires a systems view. However, control over individual interactions in complex networks is not easily achievable. Mathematical modelling provides an attractive approach for analysis of complex systems and some models may prove useful in systems pharmacology approaches to drug discovery. In this report, we used transfection screening to test interactions among 14 TERT regulatory transcription factors and their respective promoters in ovarian cancer cells. The results were used to generate a network model of TERT transcription and to implement a dynamic Boolean model whose steady states were analysed. Modelled effects of signal transduction inhibitors successfully predicted TERT repression by Src-family inhibitor SU6656 and lack of repression by ERK inhibitor FR180204, results confirmed by RT-QPCR analysis of endogenous TERT expression in treated cells. Modelled effects of GSK3 inhibitor 6-bromoindirubin-3′-oxime (BIO) predicted unstable TERT repression dependent on noise and expression of JUN, corresponding with observations from a previous study. MYC expression is critical in TERT activation in the model, consistent with its well known function in endogenous TERT regulation. Loss of MYC caused complete TERT suppression in our model, substantially rescued only by co-suppression of AR. Interestingly expression was easily rescued under modelled Ets-factor gain of function, as occurs in TERT promoter mutation. RNAi targeting AR, JUN, MXD1, SP3, or TP53, showed that AR suppression does rescue endogenous TERT expression following MYC knockdown in these cells and SP3 or TP53 siRNA also cause partial recovery. The model therefore successfully predicted several aspects of TERT regulation including previously unknown mechanisms. An extrapolation suggests that a dominant stimulatory system may programme TERT for transcriptional stability

CABeRNET: a Cytoscape app for augmented Boolean models of gene regulatory NETworks

Background. Dynamical models of gene regulatory networks (GRNs) are highly effective in describing complex biological phenomena and processes, such as cell differentiation and cancer development. Yet, the topological and functional characterization of real GRNs is often still partial and an exhaustive picture of their functioning is missing. Motivation. We here introduce CABeRNET, a Cytoscape app for the generation, simulation and analysis of Boolean models of GRNs, specifically focused on their augmentation when a only partial topological and functional characterization of the network is available. By generating large ensembles of networks in which user-defined entities and relations are added to the original core, CABeRNET allows to formulate hypotheses on the missing portions of real networks, as well to investigate their generic properties, in the spirit of complexity science. Results. CABeRNET offers a series of innovative simulation and modeling functions and tools, including (but not being limited to) the dynamical characterization of the gene activation patterns ruling cell types and differentiation fates, and sophisticated robustness assessments, as in the case of gene knockouts. The integration within the widely used Cytoscape framework for the visualization and analysis of biological networks, makes CABeRNET a new essential instrument for both the bioinformatician and the computational biologist, as well as a computational support for the experimentalist. An example application concerning the analysis of an augmented T-helper cell GRN is provided.Comment: 18 pages, 3 figure

An Extended Gene Protein/Products Boolean Network Model Including Post-Transcriptional Regulation

Background: Networks Biology allows the study of complex interactions between biological systems using formal, well structured, and computationally friendly models. Several different network models can be created, depending on the type of interactions that need to be investigated. Gene Regulatory Networks (GRN) are an effective model commonly used to study the complex regulatory mechanisms of a cell. Unfortunately, given their intrinsic complexity and non discrete nature, the computational study of realistic-sized complex GRNs requires some abstractions. Boolean Networks (BNs), for example, are a reliable model that can be used to represent networks where the possible state of a node is a boolean value (0 or 1). Despite this strong simplification, BNs have been used to study both structural and dynamic properties of real as well as randomly generated GRNs. Results: In this paper we show how it is possible to include the post-transcriptional regulation mechanism (a key process mediated by small non-coding RNA molecules like the miRNAs) into the BN model of a GRN. The enhanced BN model is implemented in a software toolkit (EBNT) that allows to analyze boolean GRNs from both a structural and a dynamic point of view. The open-source toolkit is compatible with available visualization tools like Cytoscape and allows to run detailed analysis of the network topology as well as of its attractors, trajectories, and state-space. In the paper, a small GRN built around the mTOR gene is used to demonstrate the main capabilities of the toolkit. Conclusions: The extended model proposed in this paper opens new opportunities in the study of gene regulation. Several of the successful researches done with the support of BN to understand high-level characteristics of regulatory networks, can now be improved to better understand the role of post-transcriptional regulation for example as a network-wide noise-reduction or stabilization mechanism

Inferring tree causal models of cancer progression with probability raising

Existing techniques to reconstruct tree models of progression for accumulative processes, such as cancer, seek to estimate causation by combining correlation and a frequentist notion of temporal priority. In this paper, we define a novel theoretical framework called CAPRESE (CAncer PRogression Extraction with Single Edges) to reconstruct such models based on the notion of probabilistic causation defined by Suppes. We consider a general reconstruction setting complicated by the presence of noise in the data due to biological variation, as well as experimental or measurement errors. To improve tolerance to noise we define and use a shrinkage-like estimator. We prove the correctness of our algorithm by showing asymptotic convergence to the correct tree under mild constraints on the level of noise. Moreover, on synthetic data, we show that our approach outperforms the state-of-the-art, that it is efficient even with a relatively small number of samples and that its performance quickly converges to its asymptote as the number of samples increases. For real cancer datasets obtained with different technologies, we highlight biologically significant differences in the progressions inferred with respect to other competing techniques and we also show how to validate conjectured biological relations with progression models

Gene switching rate determines response to extrinsic perturbations in the self-activation transcriptional network motif

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